This invention relates to phase-shifting (or phase-compensating) transformers that advances or retards the phase-angle relationship of one three-phase circuit with respect to another; more particularly, it relates to such transformers that are used in three-phase power and distribution systems for connecting two power systems which have different voltages and phase angles, or for controlling the power flow in a loop-shaped power system so as to minimize the transmission loss therein.
Phase-shifting (or phase-compensating) transformers are used to adjust the phase angle of an output, controlling the output within specified limits and compensating for the fluctuations of the load and input. Conventional phase-shifting transformers for three-phase power systems have generally comprised two three-phase transformer units whose cores are relatively large-sized and heavy. FIGS. 1 and 2 show, in a perspective view and a plan view thereof respectively, a typical interior structure of the essential portions of one of the two three-phase transformer units of a conventional phase shifting transformer, i.e., the main or the series transformer unit. In order to make clear the above-mentioned disadvantages of the conventional phase-shifting transformers, let us first describe the electrical structure and method of operation of phase-shifting transformers in some detail.
FIG. 3 is a circuit or wiring diagram showing a typical circuit structure of a phase-shifting transformer. The phase-shifting transformer consists of two three-phase transformer units: a main transformer unit 1 and a series transformer unit 11, each of which constitutes a three-phase transformer, a typical interior structure of which is as shown essentially in FIGS. 1 and 2. Thus, the main and the series transformer unit 1 and 11 each comprise windings which are wound on a three-phase core (i.e. a core having three independent magnetic circuits each linking with one of the three phases of the windings of the transformer unit).
The main transformer unit 1 comprises three three-phase windings: a Y-connected primary winding 2, a Y-connected secondary winding 3, and a .DELTA.-connected tertiary winding 4, each one of which comprises three phase-windings: U-phase, V-phase, and W-phase winding. The phase-windings which are in the same phase (i.e. U-, V-, or W-phase) are drawn parallel to each other in the figure and are magnetically coupled to each other via respective magnetic circuits of the core of the main transformer 1. The U-, V-, and W-phase windings of the Y-connected primary winding 2 are provided with input terminals U, V, and W, respectively, which are coupled to a three-phase power source system. On the other hand, the U-, V-, and W-phase windings of the Y-connected secondary winding 3 are provided with output terminals u, v, and w, respectively, that are coupled to the load.
The series transformer unit 11 also comprises three three-phase windings: a Y-connected phase-regulating (or phase-compensating) winding 13, a Y-connected excitation winding 14, and a .DELTA.-connected stabilizing winding 15, each one of which comprises three phase-windings in a-, b-, and c-phase, respectively; the phase-windings in the same phase (i.e., in a-, b-, or c-phase) are drawn parallel to each other in the figure, and are magnetically coupled to each other via respective magnetic circuits of the core of the series transformer 11. The three terminals of the Y-connected excitation winding 14 are coupled, via the terminals a, b, and c, respectively, to the terminals of the .DELTA.-connected tertiary winding of the main transformer unit 1, to be supplied with an exciting current of the series transformer unit 11. On the other hand, the a-, b-, and c-phase windings of the Y-connected phase-regulating winding 13, which comprise change-over taps Ta, Tb, and Tc, and contacts Sa, Sb, and Sc, are coupled, via these taps and contacts, electrically in series with the V-, W-, and U-phase windings, respectively, of the Y-connected secondary winding 3 of the main transformer unit 1, so as to adjust the phase-angle of the output voltages at the terminals u, v, and w of the secondary winding 3 of the main transformer unit 1.
The method of operation of the phase-shifting transformer having a wiring structure as shown in FIG. 3 may now be comprehended easily. When a three-phase power system is coupled to the primary winding 2 of the main transformer unit 1 via the terminals U, V, and W, so that the system or source voltages E.sub.U, E.sub.V, and E.sub.W are applied on the respective terminals, voltages are induced across the U-, V-, and W-phase winding thereof which counterbalance the system voltages E.sub.U, E.sub.V, and E.sub.W, respectively. Thus, assuming, for simplicity's sake, that the winding directions of the U-, V-, and W-phase windings are the same, magnetic fluxes .phi..sub.U, .phi..sub.V, and .phi..sub.W whose phases are displaced 120 degrees from each other, as shown in solid arrows in the phasor (or vector) diagram of FIG. 4, are induced in the respective magnetic circuits of the core of the main transformer unit 1. As a result, voltages in phase with the voltages across the phase-windings of the primary winding 2 are induced in the respective phase-windings, drawn parallel thereto, of the Y-connected secondary and the .DELTA.-connected tertiary windings 3 and 4.
Since the tertiary winding 4 is .DELTA.-connected while the primary winding 2 is Y-connected, the voltages E.sub.A, E.sub.B, and E.sub.C, with respect to the ground, at the terminals a, b, and c of the tertiary winding 4 are retarded 30 degrees in their phases with respect to the voltages E.sub.U, E.sub.V, and E.sub.W, with respect to the ground (i.e. the voltage at the neutral point of Y-connection), at the terminals U, V, and W of the primary winding 2. Further, since the excitation winding 14, coupled to the terminals a, b, and c, is Y-connected, the voltages E.sub.A, E.sub.B, and E.sub.C at the terminals a, b, and c with respect to the ground are applied across the a-, b-, and c-phase windings, respectively, of the excitation winding 14. Hence, the phases of the voltages applied across the a-, b-, and c-phase windings of the excitation winding 14 of the series transformer unit 11 are retarded by 30 degrees with respect to the phases of the voltages across the U-, V-, and W-phase windings of the primary 2, secondary 3, and tertiary winding 4 of the main transformer unit 1.
Now, in order to make the explanation simpler, let us assume that the winding directions of the three phase-windings (i.e. a-, b-, and c-phase windings) of the excitation winding 14 of the series transformer unit 11 are the same. As shown in the phasor or vector diagram of FIG. 5, three magnetic fluxes .phi.a, .phi.b, and .phi.c (represented by solid arrows), which are displaced 120 degrees from each other and are retarded by 30 degrees with respect to the magnetic fluxes .phi..sub.U, .phi..sub.V, and .phi..sub.W (represented by broken arrows), respectively, of the main transformer unit 1, are induced in the respective magnetic circuits of the core of the series transformer unit 11 which are linking the a-, b-, and c-phase windings, respectively, of the excitation winding 14. As a result, voltages Ea, Eb, Ec in phase with the voltages across the a-, b-, and c-phase windings of the excitation winding 14 are induced in the a-, b-, and c-phase windings, respectively, of the regulating winding 13 and the stabilizing winding 15, which are drawn parallel thereto and magnetically coupled therewith, respectively.
Thus, the voltages developed across the a-, b-, and c-phase windings of the regulating winding 13, the excitation winding 14, and the stabilizing winding 15 of the series transformer unit 11 are retarded 30 degrees in their phases with respect to the voltages across the U-, V-, and W-phase windings of the windings 2 through 4 of the main transformer unit 1. Consequently, as shown in the phasor diagram of FIG. 6, the voltages Ea, Eb, and Ec induced respectively across the lengths of the a-, b-, and c-phase windings of the phase-regulating winding 13 that are electrically coupled in series with the V-, W-, and U-phase windings of the secondary winding 3 are retarded by 30 degrees with respect to the system voltages E.sub.U, E.sub.V, and E.sub.W (represented by broken arrows in the figure), respectively. Hence, the same voltages Ea, Eb, and Ec developed in the regulating winding 13 are advanced by 90 degrees with respect to the voltages E.sub.V, E.sub.W, and E.sub.U, respectively. Further, as discussed above, the voltages 20, E.sub.V ', E.sub.W ', E.sub. U ' induced across the the V-, W, and V-phase windings of the secondary winding 3 are in phase with the source voltages E.sub.V, E.sub.W, E.sub.U. Thus, the above voltages Ea, Eb, and Ec are advanced by 90 degrees with respect to the voltages E.sub.V ', E.sub.W ', and E.sub.U ' induced across the respective phase windings of the secondary winding 3. Since the a-, b-, and c-phase windings of the regulating winding 13 are electrically coupled in series with the V-, W-, and U-phase windings, respectively, of the secondary winding 3, the voltages Eu, Ev, Ew with respect to the ground at the terminals u, v, and w of the secondary winding 3 are given as vector sums of Ea and E.sub.V ', Eb and E.sub.W ', and Ec and E.sub.U ', respectively, as shown in FIG. 6; namely: EQU Ev=Ea +E.sub.V ', EQU Ew=Eb+E.sub.W ',
and EQU Eu=Ec+E.sub.U '.
As a result, the phases of the voltages Eu, Ev, and Ew with respect to the ground at the output terminals u, v, and w of the secondary winding 3 are advanced or retarded with respected to the system voltages E.sub.U, E.sub.V, and E.sub.W, respectively, by a phase angle .theta. the magnitude of which can be adjusted by varying the magnitude of the voltages Ea, Eb, and Ec. Whether the output voltages Eu, Ev, and Ew are advanced or retarded depends on the polarities of the serial connections of the voltages Ea, Eb, and Ec (i.e, on the positions of the contacts Sa, Sb, and Sc). Thus, by adjusting the positions of the contacts Sa, Sb, and Sc and those of the taps Ta, Tb, and Tc by means of an onload tap changer (not shown), the phases of the output voltages Eu, Ev, and Ew of the secondary winding 3 can be adjusted arbitrarily.
In the above discussion of the operation of the phase-shifting transformer having the wiring structure of FIG. 3, it was assumed, for simplicity's sake, that winding directions of the phase-windings 2 through 4 of the main transformer unit 1, or those of the phase-windings 13 through 15 of the series transformer unit 11, are the same. However, as is obvious to those skilled in the art, this assumption is not essential. Although the directions of the magnetic fluxes may be reversed, the relationships of the voltage phasors shown in FIG. 6 hold good irrespective of the winding directions of the respective phase-windings. Hence, the principles of operation are essentially as described above even if the V-phase windings within the main transformer unit 1 or b-phase windings within the series transformer unit 11, for example, are wound in the opposite directions with respect to other phase-windings of the transformer unit 1 or 11.
Referring once again to FIGS. 1 and 2, let us now describe the physical structure of the essential interior portions of the main and the series transformer units 1 and 11. FIGS. 1 and 2 show, in a perspective and a plan view, respectively, the interior of the main transformer unit 1 alone. The series transformer unit 11 has essentially the same interior structure, except that the U-, V-, and W-phase windings of the main transformer unit 1 are replaced by the a-, b-, and c-phase windings, respectively. Thus, in the following, only the structure of the main transformer unit 1 is described in reference to FIGS. 1 and 2; the whole phase-shifting transformer having a wiring structure of FIG. 3 is constituted by two such transformer units electrically coupled to each other according to the wiring structure shown in FIG. 3.
The combined U-, V-, and W-phase winding units 22U, 22V, and 22W, which consist of the combination of U-, V-, and W-phase windings, respectively, of the primary, secondary, and tertiary windings 2 through 4, are wound around respective main leg portions 23 of a core 21; however, the winding direction of the combined V-phase winding 22V is reversed with respect to those of the combined U- and W-phase windings 22U and 22W. Thus, since the figures show a shell-type core structure, the combined U-, V-, and W-phase windings 22U, 22V, and 22W each link with a magnetic circuit consisting of a pair of closed flux paths for passing the main magnetic fluxes .phi..sub.U, -.phi..sub.V, and .phi..sub.W therethrough, respectively, wherein the flux paths of any two adjacent magnetic circuit have portions 24 (referred to hereinafter as interphase portions) common to both, which are shaded in FIG. 2.
As stated above, the winding direction of the combined V-phase winding 22V is reversed with respect to others. Thus, as shown by a broken arrow in FIG. 4, the main magnetic flux -.phi..sub.V, linking with the combined V-phase winding 22V and flowing in the direction as shown by the arrow -.phi..sub.V in FIG. 2, is displaced by a phase angle of 60 degrees with respect to the magnetic fluxes .phi..sub.U and .phi..sub.W linking with combined U- and W-phase windings 22U and 22W, respectively. The absolute magnitudes of these three main magnetic fluxes .phi..sub.U, -.phi..sub.V, and .phi..sub.W are equal to one another.
Now, let us consider the magnitudes of the differential magnetic fluxes flowing through the interphase portions 24 (shaded in the figure) of the core 21 that are common to the adjacent magnetic circuits for the magnetic fluxes .phi..sub.U, -.phi..sub.V, and .phi..sub.W, respectively, within the core 21. It is easy to see from FIG. 2 that the differential magnetic fluxes passing through the interphase portions 24 of the core 21 are given by a vector difference between two magnetic fluxes flowing through the two adjacent magnetic circuits. Thus, the differential magnetic flux .phi..sub.UV passing through the interphase portion 24 between the two magnetic circuits linking respectively with the combined U- and V-phase windings 22U and 22V is given by the vector difference between the two adjacent main magnetic fluxes .phi..sub.U and -.phi..sub.V : EQU .phi..sub.UV =.phi..sub.U -(-.phi..sub.V).
Further, the differential magnetic flux .phi..sub.VW passing through the interphase portion 24 between the two magnetic circuits linking respectively with the combined V- and W-phase windings 22V and 22W is given by the vector difference between the two adjacent main magnetic fluxes -.phi..sub.V and .phi..sub.W : EQU .phi..sub.VW =-.phi..sub.V -.phi..sub.W.
The vectorial relationships between these main and differential magnetic fluxes are graphically represented in FIG. 4, wherein the three main magnetic fluxes .phi..sub.U, -.phi..sub.V have the same absolute magnitudes and are separated by 60 degrees from each other. Thus, as is apparent from the figure, the absolute magnitudes of the differential magnetic fluxes .phi..sub.UV and .phi..sub.VW passing through the interphase portions 24 of the core 21 are equal to that of the absolute magnitudes of the main magnetic fluxes .phi..sub.U, -.phi..sub.V, and .phi..sub.W.
The cross-sectional areas of magnetic circuits within a transformer must be sufficiently large to pass therethrough the magnetic fluxes generated therein. Thus, the cross-sectional areas of the interphase portions 24 should be designed equal to those of the main leg portions 23 of the core 21. Since the thickness or height H of the core 21 is uniform, the width D.sub.2 of the interphase portions 24 of the core 21 are designed equal to the width D.sub.1 of its main leg portions 23. The situation is the same with the series transformer 11 which has fundamentally the same core structure.
Thus, due to the core structure described above, the conventional phase-shifting transformer has the following disadvantages: First, since the transformer is devides into two three-phase transformer units, i.e., the main and the series tranformer units, it is large-sized and requires much time and labor in the assembly, transportion, and installation thereof. In addition, equipment for the transformer, such as tanks, bushings, and protective relays, must be provided separately for the two units. Even if the two transformer units are accomodated in a single tank, the essential interior structure remains the same, with the result that the production cost cannot be materially reduced. The large outer dimension of the tank, however, results in the increased cost in the transportation, etc.
A second disadvantage of the conventional phase-shifting transformer, which is related to the above first disadvantage and makes it even worse, is that the cores of the two transformer units are heavy and large-sized even taken by themselves due to the fact that their interphase portions must have large cross-sectional areas to allow the passage of the differential magnetic fluxes therethrough.